Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in fully simplified slope-intercept form is [tex]y=\frac{1}{4} x-1[/tex].
What is a slope intercept form?A line is defined by the equation y = mx + b, which is also known as the slope-intercept form. When the line is graphed, m represents the slope and b the point at which the line intersects the y-axis.
For calculating the slope, the formula used is [tex]m=\frac{x_{2} -x_{1} }{y_{2} -y_{1} }[/tex]
From the graph we see that the points are (4,0) and (0,-1).
Substituting the points in the formula,
[tex]m=\frac{x_{2} -x_{1} }{y_{2} -y_{1} }\\m=\frac{-1-0}{0-4} \\m=\frac{-1}{-4} \\m=\frac{1}{4}[/tex]
We know that, the equation of a line in point slope form, where (x₁, y₁) is the point and slope m is:
(y – y₁) = m(x – x₁)
Here, (x₁, y₁)= (4,0)
Substitute the value of m and any coordinate into the formula y−y₁=m(x−x₁)
[tex]y-0=\frac{1}{4} (x-4)\\y=\frac{1}{4} x-1[/tex]
Therefore, the equation of the line in fully simplified slope-intercept form is [tex]y=\frac{1}{4} x-1[/tex].
To learn more about the slope intercept form, visit:
https://brainly.com/question/9682526
#SPJ9
the volume of water is usually distributed with a mean of 62ml and standard deviation of 40ml. What is the probability that the volume will be greater than 90ml?
The probability of the volume of water being over 90 ml is 24.10%.
What exactly is the standard normal distribution?A symmetric probability distribution only with equal mean, mean, as well as mode values is known as a standard normal distribution.A statistical table as well as computer software is used to estimate the likelihood of a standard normal distribution.For the given question;
The mean of the sample is; μ = 62 ml.
The standard distribution is; σ = 40 ml.
The probability of the values must lie more than 90 ml.
Thus,
P(x > 90) = P[ (x - μ)/ σ ]
Substitute the values;
P(x > 90) = 1 - P[ (90 - 62)/ 40]
P(x > 90) = 1 - P[0.7]
P(x > 90) = 1 - 0.758
P(x > 90) = 0.2410
P(x > 90) = 24.10%
Therefore, the probability that the the volume of water will be greater than 90 ml is 24.10%.
To know more about the standard normal distribution, here
brainly.com/question/4079902
#SPJ9
The value of the 7 in 57,264 is ten times greater than the value of the 7 in which of these numbers?
A. 17,810
C. 78,893
B. 61,715
D. 95,371
C.78893
Step-by-step explanation:
-_-_+_(*;#-✓✓
Joshua purchased a game card for the arcade for a total of $20. He played three basketball hoop games for $2.25 each and two rounds of air hockey for $1.75 each. How much did he have left on the game card?
1.)$ 13.50
2.)$ 10.25
3.)$ 9.75
4.)$ 6.75
Answer:
b
Step-by-step explanation:
Joshua had $9.75 left on the game card (option 3).
Joshua's expenses on the game card can be calculated as follows:
Cost of playing three basketball hoop games = 3 games * $2.25/game
Cost of playing three basketball hoop games = $6.75
Cost of playing two rounds of air hockey = 2 rounds * $1.75/round
Cost of playing two rounds of air hockey = $3.50
Total expenses = $6.75 + $3.50
Total expenses = $10.25
Joshua originally had $20 on the game card, and he spent $10.25. To find out how much he had left, subtract his expenses from the original amount:
Amount left = $20 - $10.25
Amount left = $9.75
So, Joshua had $9.75 left on the game card.
The correct answer is 3.) $9.75.
To know more about expenses:
https://brainly.com/question/29850561
#SPJ3
Which number line represents the solutions to lx + 4) = 2?
O
O
O
←
+++
-7 -6 -5 -4 -3 -2 -1 0
1 2
+
←
+++ ++
-7 -6 -5 -4 -3 -2 -1 0 1
┫
+
+
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
++
+
-7 -6 -5 -4 -3 -2 -1 0 1
2
3
2
+3
+
3
4
4
5
▬▬▬▬▬▬▬▬
4 5
6 7
4
+ +
6
7
5 6 7
++
5 6 7
+
Please help solve question
Answer:
a) [tex]x=\frac{15}{p}[/tex]
b) x=[tex]-3[/tex]
Step-by-step explanation:
First, you distribute the 4 to open the parentheses.
[tex]4px+4=64[/tex]
Subtract 4 to both sides:
[tex]4px=60[/tex]
Divide by 4p on both sides:
[tex]x=\frac{60}{4p}[/tex]
[tex]x=\frac{15}{p}[/tex]
For the second part, substitute the value of p.
[tex]x=\frac{15}{-5}[/tex]
[tex]x=-3[/tex]
Find an equation of the tangent line to the curve at the given point.
y = x³ - 3x + 1, (3, 19)
Answer:
y=24x-53.
Step-by-step explanation:
1) the slope-interception view of the required tangent line is
y=slope*x+interception;
2) y'=3x²-3;
3) slope=y'(3), then slope=3*3²-3=24;
4) the required equation of tangent line has the form
y=24x+interception;
5) to calculate the interception it is needed to substitute the given coordinates (3;19) into this equation:
19=24*3+interception; ⇒ interception=-53;
6) finally, the required equation is y=24x-53.
0.02,0.2,2,20,200, what is next
Answer:
0.2
Step-by-step explanation:
Answer: 2000
Step-by-step explanation:
The pattern is multiplying by 10. Therefore, 200 x 10= 2000
HELP ME OUT PLEASE!!
What does the y-intercept of the graph represent?
O It was 8°F when recording began
O There is a change of 4°F every hour
O There is a change of 2 °F eve every hour
O Maximum temperature is 20°F
Answer:
see explanation
Step-by-step explanation:
the y- intercept 8 occurs when time = 0
that is it was 8° F when recording began at time = 0
7/20 convertir de fracción a decimal
Answer: 0.35
Step-by-step explanation:
7/20 = 0.35
0.35 x 20 = 7
which box and whiskers plot matches the data, 23, 32, 20, 13, 27, 36, 29, 38 23, 15, 30, 18, please its a test
Answer:
Option C
Step-by-step explanation:
Given the data set, 23, 32, 20, 13, 27, 36, 29, 38, 23, 15, 30, 18, to find out which box-and-whisker plot matches the data, let's work out the 5-number summary needed for constructing a box plot.
The five-number summary includes the min, Q1, median, Q3 and max value.
Let's find them.
First, order the data set from the least to the largest
13, 15, 18, 20, 23, 23, 27, 29, 30, 32, 36, 38
Min = 13
Max = 38
Median = (23 + 27) ÷ 2 = 50 ÷ 2 = 25
Q1 = (18 + 20) ÷ 2 = 38 ÷ 2 = 19
Q3 = (30 + 32) ÷ 2 = 62 ÷ 2 = 31
The box-and-whiskers plot will have the description given in option C.
What is 4 gal 6 qt 112 oz in standard notation?
The value of 4 gal 6 qt 112 oz expressed in standard notation is; 6.375
How to express in Standard Notation?
Standard notation of a number is defined as when a number is written with only number digits. This is the typical way to write numbers since words are not used in standard number notation.
Now, from conversions, we know that;
1 oz = 0.0078125 gallons
1 qt = 0.25 gallons
Thus, 4 gal 6 qt 112 oz expressed in gallons is;
4 + (6 * 0.25) + (112 * 0.0078125)
= 4 + 1.5 + 0.875
= 6.375
Read more about Standard Notation at; https://brainly.com/question/1313442
#SPJ1
The governor of state A earns $54,900 more than the governor of state B. If the total of their salaries is $310,850, find the salaries of each.
Step-by-step explanation:
Let the earning of governor of state B be x then
we have,
Earning of A = 54900 + x
Earning of B = x
according to question,
Earning of A + Earning of B = 310850
54900 + x + x = 310850
2x = 255950
x = 127975
earning of A = 182875$
earning of B = 127975$
algebra
(3x)^3 3^3 x^3 =????
Answer: 729x^6
Step-by-step explanation: I got this answer because I first multiplied the 3^3 which is 27
then the equation is 27x^3 times 3^3x^3. Then you do the same thing on the other side which is 27x^3. So 27x^3 times 27x^3. After that you multiple 27 and 27 which is 729, don’t forget your x^3 and x^3 which is x^6 so your answer is 729x^6.
Find the sum and choose the correct answer.
2n³+4n²-7 and -n³-8n-2
²³+4n²-87-9
On²³-41²-9
O-n³+4n²-80-9
On²+4n²-8n-5
Answer:
Your answer is n^3 + 4n^2 - 8n - 9
Hope this helps! <3
Triangle PQR has vertives P(2, -4), Q(4, -5), and R(7, -2). It is translated 6 units left and 3 units up to produce Triangle P'Q'R'. Complete table.
The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.
What are the locations of the vertices of the triangle after applying rigid transformations?
In this problem we know the three vertices of a triangle on a Cartesian plane and we must determine the coordinates of its image by applying rigid transformations. According to the statement, the vertices of the image are obtained by applying a translation formula:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
P(x, y) - Original pointP'(x, y) - Resulting point T(x, y) - Translation vectorIf we know that P(x, y) = (2, - 4), Q(x, y) = (4, - 5), R(x, y) = (7, - 2) and T(x, y) = (- 6, 3), then the coordinates of the vertices of the image are:
P'(x, y) = (2, - 4) + (- 6, 3)
P'(x, y) = (- 4, - 1)
Q'(x, y) = (4, - 5) + (- 6, 3)
Q'(x, y) = (- 2, - 2)
R'(x, y) = (7, - 2) + (- 6, 3)
R'(x, y) = (1, 1)
The coordinates of the triangle P'Q'R' is P'(x, y) = (- 4, - 1), Q'(x, y) = (- 2, - 2) and R'(x, y) = (1, 1), respectively.
To learn more on rigid transformations: https://brainly.com/question/1761538
#SPJ1
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ACDE=AOPQ?
Check all that apply.
AA
E
A. LL
B. AAS
C. SAS
D. LA
E. HL
F. ASA
Answer is ADEF
Given that, two right tringle = R + ΔHEL , R +ΔPME
Hypotenuse equal , A set of corresponding right angles are equal.{HL};
LL=LE
So ∠E(M tringle HEL)∠LM (M tringle PME)
∠H=∠P 90°
∠L=∠E ⇒AAS
HE PM or LE =EM
∠E = ∠M
EL = ME ⇒ASA
∠L = ∠E
HF = PM
∠E = ∠M ⇒SAS
EL = ME
Hence choose A.D.E.F
{Determination of congruence of right tringle }
explanation of Determination of congruence of right tringle
A plane figure bounded by three finite line segments to form a closed figure is known as a triangle. A right-angled triangle is a special case of the triangle. In a right-angled triangle, one of the interior angles measures 90°. Two right triangles are said to be congruent if they are of the same shape and size. In other words, two right triangles are said to be conger
Learn more about Determination of congruence of right tringle here: brainly.in/question/10800663
SPJ9
Solve For x
[tex] \tt \red{4x + 2 = -8}[/tex]
Thank uh ~
Answer:
The answer will be -5/2.
Step-by-step explanation:
[tex]4x + 2 = - 8 \\ subtracting \: 2 \: from \: each \: sides \: we \: get \\ 4x + 2 - 2 = - 8 - 2 \\ 4x = - 10 \\ diving \: both \: sides \: by \: 4 \: we \: get \\ \frac{4x}{4} = \frac{ - 10}{4} \\ x = \frac{ - 5 \times 2}{2 \times 2} \\ x = \frac{ - 5}{2} [/tex]
Mary's birthday is between June 13 and June 23. The date of her birthday is not an even number. The sum of the digits is 3. When is Mary's birthday
Answer:
Step-by-step explanation:
possible two digit numbers with sum 3 are 03,12,21,30
only 21 is between 13 and 23.
Mary's birthday is June 21.
PLS ANSWER. The questions is attached. Dont' put like I dont' know the answer if u don't know don't answer pls.
Answer:
x = 2.4
Step-by-step explanation:
see image for explanation.
Hope it helps
radius of a circle is 5 units what is the diameter
1/5 + 1/3x > 1/2x - 1/4
The common denominator represent the value is X<2.7.
Get every x term on the right side and every constant term on the left to begin.
1/5+1/3 X>1/2 X-1/4
1/5+1/4+1/3 X>1/2 X
1/5+1/4>1/2 X-1/3 X
The two halves of a fraction are the numerator and the denominator. Any arithmetic operation involving two or more fractions, such as addition or subtraction, is possible if the denominators of the two fractions are the same. To this, the phrase "common denominator" relates.
When two fractions have the same denominator, we refer to them as having common denominators. Common denominators facilitate fractional operations like comparison, addition, and subtraction.
Give common denominators to the terms on each side now.
4/20+5/20>3/6 X-2/6 X
9/20>1/6 X
By multiplying both sides by 6, we may now.
27/10>X
2.7>X
Hence, the common denominator value is X<2.7.
To learn more about common denominator, visit:
brainly.com/question/11516652
#SPJ9
Determine whether the given ordered pair is a solution of
the system of equations.
(8, 7); -x+y= - 1
6x + y = 41
Answer:THE ANSWER IS NO.
Step-by-step explanation:
As we have given that x=8 and y=7
put theses values in given equations :-
-x + y= -1
-8+7= -1,true
But, for 6x+y=41
We get 6*8+7=41
55 ≠41
Hence the answer is NO.
Answer:
Step-by-step explanation: if the ordered pair (8,7) is a solution of a system of equations; the values x=8, y=7 substituted in the system must make both equations true. -8+7=-1 -1=-1 √ 6×8+7=41 48+7=41 55=41(8,7) is not a solution of the systems.
Can someone help me out please??
Answer:
1. 7/8
2. 1/2
Step-by-step explanation:
y2-y1 /x2-x1 = slope
1. points: (-4,-4) and (4,3)
M = (3+4)/(4+4)
M=7/8
2. points: (-5,-3) and (3,1)
M = (1+3)/(3+5)
M = 4/8 or 1/2
Find the -intercept and the slope of the line 4x8y=3. Write your answers in simplest form.
The slope of the straight line is -1/2 whereas the y-intercept is 3/8.
What is defined as the equation of line in slope intercept form?Recognize that the y-intercept is the point at which the graph intersects the y-axis; that's where we usually begin.
Determine the slope first, then the y-intercept. For the time being, just consider if the slope is either positive or negative.The following are the variables that we will begin to use in our function:slope = mb = the y-interceptThe formula is y = mx + b. The variables x and y remain alphabets, but m and b have been replaced by numbers (for example, y = 2x + 4, slope = 2, and y-intercept = 4).Because the two quantities in the equation are now the slope and the intercept, this equation is known as the slope-intercept form.
y = mx + b
Remember that the slope (m) is the number multiplied by x, while the intercept (b) is indeed the number added or subtracted.
The given equation is;
4x + 8y = 3
Re-arranging the equation;
8y = -4x + 3
Divide the whole equation by 8.
y = -4x/8 + 3/8
Further simplifying;
y = -x/2 + 3/8
Comparing the result with the general form of equation.
m = -1/2; which is the slope.
c = 3/8; which is the y-intercept.
Thus, the values for slope and y-intercept are estimated.
To know more about the slope-intercept form, here
https://brainly.com/question/9675233
#SPJ9
The correct question is-
Find the -intercept and the slope of the line 4x + 8y=3. Write your answers in simplest form.
Write a linear cost function for the situation. Identify all variables used.
A parking garage charges 3 dollars plus 45 cents per half-hour.
Identify all variables used. Choose the correct answer below.
Part 2 of 2
O A. C(x) represents the number of hours the parking garage was used after paying x dollars.
B. C(x) represents the number of half-hours the parking garage was used after paying x dollars.
C. C(x) represents the cost for using the parking garage for x half-hours.
OD. C(x) represents the cost for parking x cars in the parking garage.
A linear cost function for the situation is C(x) =
(Use integers or decimals for any numbers in the expression.)
The length of a rectangle is twice its width.
If the perimeter of the rectangle is 48 ft, find its length and width.
Formula we use,
→ P = 2(L + W)
Then the value of L and W is,
→ P = 2(L + W)
→ 48 = 2(2x + x)
→ 2(3x) = 48
→ x = 48/6
→ [ x = 8 ]
Then the width will be,
→ W = x = 8 ft
Hence, the width is 8 ft.
Now the length will be,
→ L = 2x = 2(8) = 16 ft
Therefore, the length is 16 ft.
x 10 = 23
6+x=-11
x-5 = -5
Answer: Algebra. Equation Solver. Step 1: Enter the Equation you want to solve into the editor. The equation calculator allows you to take a simple or complex equation and solve by best method possible. Step 2: Click the blue arrow to submit and see the result!
Step-by-step explanation:
eight plus the quotient of a number and 3 is 75
8 + x / 3 = 75
Minus 8 on both sides
x / 3 = 67
Multiply by 3 on both sides.
x = 201
One person has 1700 more than another person .Between then,they have a total of 10500. How much does each person have?
Answer:
One person will have 6100 and the other will have 4400.
Step-by-step explanation:
10500/2 = 5250
1700/2 = 850
5250+850 = 6100
10500-6100 = 4400
Check Answer:
6100+4400 = 10500
6100-4400 = 1700
